One failure mode this could potentially introduce that wasn’t present earlier: team members will necessarily end up seeing the notification about the motion-to-FCP, and looking at it, in some order. Let’s say the team has 6 members. If the first four who see the notification all tick their boxes, then the proposal will enter FCP before the last two have any opportunity to register a concern, even if they might’ve had one.
Of course, if the time scale this happens in is something like “one month”, then that was the whole point. But in theory nothing prevents it from taking place in the course of a day, either. If this is considered to be a cause for concern, a solution might be to modify the rule to something like “either (a) all the boxes have been checked, or (b) all-but-two have been, and at least (e.g.) a week has elapsed” (plus the other conditions from before).
(The other solution is to just @fcp cancel in that situation of course, but that might seem a bit heavy-handed depending on how frequently it happens.)